# Generalised Jantzen filtration of Lie superalgebras I

@article{Su2010GeneralisedJF, title={Generalised Jantzen filtration of Lie superalgebras I}, author={Yucai Su and R. B. Zhang}, journal={arXiv: Representation Theory}, year={2010} }

A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan-Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of…

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